Solution:
The side lengths can only be classified as a right triangle if it is a Pythagorean triple. To classify the side lengths as a Pythagorean triple, it must satisfy "c² = b² + a²".
Where:
- c = Longest side (Hypotenuse)
- b = Leg
- a = Leg
Checking (5, 12, 13):
- c² = b² + a²
- 13² = 12² + 5²
- 169 = 144 + 25
- 169 - 144 = 25
- 25 = 25 (Yes)
Checking (12, 35, 20√3):
- (20√3)² = 35² + 12²
- (20√3)(20√3) = 1225 + 144
- 1200 = 1225 + 144 (No)
Checking (5, 10, 5√5):
- (5√5)² = 10² + 5²
- 125 = 100 + 25
- 125 = 125 (Yes)
Checking (8, 12, 15):
- 15² = 12² + 8²
- 225 = 144 + 64 (No)
Checking (20, 99, 101):
- 101² = 99² + 20²
- 10201 = 9801 + 400
- 10201 = 10201 (Yes)
